This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 Excerpt: ...we have tan IB--a)=tan B--tan a=(Bg) COS B COS a For the element da of a meridian on the projection we have J ds cos a ds being the corresponding length on the sphere; this is, for a sphere, dr=re70Vl+(o88in0 and consequently a=r f(l+u' sin 0) J do This is an elliptic integral, and depends for its solution on the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1882 Excerpt: ...we have tan IB--a)=tan B--tan a=(Bg) COS B COS a For the element da of a meridian on the projection we have J ds cos a ds being the corresponding length on the sphere; this is, for a sphere, dr=re70Vl+(o88in0 and consequently a=r f(l+u' sin 0) J do This is an elliptic integral, and depends for its solution on the rectification of an arc of an ellipse with semi-axes=r Vl--a and r respectively. If the meridians are to be projected into right lines perpendicular to the equator, we must make 5 a function of o only, thus: n and p' (o)=n cos 0 then i)=p (0)=nsin 0 This projection is a projection of Lambert's, called by G-rmain " Lambert's isocylindric projection." For m=l and a radius of r these formulas are?=ra) 7!=rsin0 We have thus a projection consisting of a series of equidistant parallels, straight lines at right angles to the equator, representing the meridians, and another series of parallels at right angles to the first, whose distances from the equator vary as sin 0, representing the parallels of latitude. The value of 6 is, for the sphere, 0=r'cos 0, and for the spheroid ii_-J(l--e)cos0 (lsin Of making sin 0=x Then /"? __ r cos 0 duje /l-?sin2"? and consequently, -r (1-0 /(i=tw- This is, of course, an elliptic integral, but as it is quite simple we may reduce it a little further. Passing at once to the usual notation employed in elliptic functions, As c is the modulus, VI--? is the complementary modulus, and as usual write it e'; then do Denoting as usual the elliptic integral of the second kind by E(0), the modulus being understood to be e, we obtain for ij . . ssin0 cos 0, =rE(0) The further discussion of this general value of ij would only be interesting from a purely mathematical point of view; so we sh...
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Add this copy of A Treatise on Projections to cart. $19.72, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
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Add this copy of A Treatise on Projections to cart. $29.16, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of A Treatise on Projections to cart. $47.02, new condition, Sold by Revaluation Books rated 4.0 out of 5 stars, ships from Exeter, DEVON, UNITED KINGDOM, published 2009 by BiblioBazaar.
Add this copy of A Treatise on Projections to cart. $47.02, new condition, Sold by Revaluation Books rated 4.0 out of 5 stars, ships from Exeter, DEVON, UNITED KINGDOM, published 2008 by BiblioBazaar.
